He says the welfare system is "fuelling vices and impoverishing us all', and accuses the bishops of ignoring popular opinion by opposing the cap.

The government has insisted it will press ahead with the policy.

It wants to cap benefits at £500 a week for working-age families - equivalent to the average wage of £26,000 earned by working households - and £350 a week for single adults without children.

'Mortgaging the future'

But five bishops, led by the Bishop of Ripon and Leeds, the Rt Rev John Packer, tabled an amendment to the Welfare Reform Bill, arguing that the cap discriminated against families with several children.

They called for child benefit to be excluded from it - and were backed by Labour, crossbench and some Liberal Democrat peers in the House of Lords on Monday, meaning the amendment was carried by 252 votes to 237.

But writing in the Daily Mail, Lord Carey - who was Archbishop of Canterbury between 1991 and 2002 - said the bishops "cannot lay claim to the moral high-ground".

"Considering that the system they are defending can mean some families are be able to claim a total £50,000 a year in welfare benefits, the bishops must have known that popular opinion was against them, including that of many hard-working, hard-pressed churchgoers," he wrote.

"The sheer scale of our public debt - which hit £1 trillion yesterday - is the greatest moral scandal facing Britain today. If we can't get the deficit under control and begin paying back this debt, we will be mortgaging the future of our children and grandchildren."

Lord Carey praised the efforts of Work and Pensions Secretary Iain Duncan Smith - whom he called a "committed Christian" - to overhaul a benefits system which, at its worst, "rewards fecklessness and irresponsibility".

He argued the cost of benefits was "increasingly stoking social division" among the "squeezed middle, who feel resentment at the 'handouts' given to the long-term unemployed".

And he said the welfare system, originally designed to tackle "want, disease, ignorance, squalor and idleness", had become an "industry of gargantuan proportions which is fuelling those very vices and impoverishing us all".

'Sensible way'

On Tuesday, Deputy Prime Minister Nick Clegg said ministers would seek to overturn the Lords defeat when the welfare bill returns to the Commons.

He said the "vast majority" of people supported the cap because it was "fair to say you can't receive more in benefits than if you were to earn £35,000 before tax".

Welfare Reform Bill

Has completed its Commons stages and is now in the Report (penultimate) stage in the Lords

Ministers have already said they they will overturn Lords defeats in Commons

Unless and until agreement on differences is reached the bill is likely to "ping-pong" between the Lords and Commons

But he sought to reassure those worried about "transitional arrangements" - including his party's former leader Lord Ashdown - that the cap would be would be implemented "in a sensible way".

Labour backed the bishops' amendment after its own - to exclude people at risk of homelessness from the cap - failed to get enough support.

However, the party says it is not opposed to the idea of a cap in principle, and wants to see it introduced in the right way.

Monday's vote was the latest in a series of on the government's flagship Welfare Reform Bill - peers have also voted down changes to Employment Support Allowance. The government has made some concessions but says it intends to overturn the defeats in the Commons.

The government says 67,000 households, more than half of which are in London, can expect to lose £83 a week when it is brought in.

The legislation affects England, Wales and Scotland. Northern Ireland has its own social security legislation, but it is expected that what is approved at Westminster would be introduced there too.